Solve y=-2sqrt{-x}+5

$$y = - 2 \sqrt { - x } + 5$$

Solve for x

$$x=-\frac{\left(5-y\right)^{2}}{4}$$

$$\frac{5-y}{2}\geq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$-2\sqrt{-x}+5=y$$

Subtract 5 from both sides.

$$-2\sqrt{-x}=y-5$$

Divide both sides by -2.

$$\frac{-2\sqrt{-x}}{-2}=\frac{y-5}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$\sqrt{-x}=\frac{y-5}{-2}$$

Divide y-5 by -2.

$$\sqrt{-x}=\frac{5-y}{2}$$

Square both sides of the equation.

$$-x=\frac{\left(5-y\right)^{2}}{4}$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\left(5-y\right)^{2}}{-4}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\left(5-y\right)^{2}}{-4}$$

Divide \frac{\left(-y+5\right)^{2}}{4} by -1.

$$x=-\frac{\left(5-y\right)^{2}}{4}$$

Solve for x (complex solution)

$$x=-\frac{\left(5-y\right)^{2}}{4}$$

$$y=5\text{ or }arg(\frac{5-y}{2})<\pi$$

Solve for y

$$y=-2\sqrt{-x}+5$$

$$x\leq 0$$